Question

for exercises 14-15, write an equation that matches each scenario. 14. mario is 75 miles from his home. he drives 30 miles per hour to get home. write an equation to represent how far mario is from his home. 15. jayla has 12 tulip bulbs planted. she plants 3 bulbs each minute. write an equation to represent many tulip bulds jayla plants over time, in minutes.

Explanation:

Exercise 14

Step1: Define variables

Let \( t \) be the time in hours and \( y \) be the distance from home in miles.

Step2: Analyze the scenario

Initial distance from home is 75 miles. He drives towards home at 30 miles per hour, so the distance decreases by \( 30t \) miles over time \( t \).

Step3: Form the equation

The distance \( y \) from home is initial distance minus the distance covered: \( y = 75 - 30t \)

Exercise 15

Step1: Define variables

Let \( t \) be the time in minutes and \( y \) be the total number of tulip bulbs planted.

Step2: Analyze the scenario

Initial number of bulbs is 12. She plants 3 bulbs per minute, so the number of bulbs planted over time \( t \) is \( 3t \).

Step3: Form the equation

Total bulbs \( y \) is initial bulbs plus bulbs planted: \( y = 12 + 3t \)

Answer:

s:

1. \( \boldsymbol{y = 75 - 30t} \) (where \( t \) is time in hours, \( y \) is distance from home in miles)
2. \( \boldsymbol{y = 12 + 3t} \) (where \( t \) is time in minutes, \( y \) is total tulip bulbs planted)